Adam who is 20 years old is 4 times as old as Mary. What will be Mary's age when Adam is twice as old as her ?

Options

A. (a) 35 years
B. (b) 15 years
C. (c) 30 years
D. (d) 17 years

Explanation

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Identify the Current Ages:**
- Adam's current age = 20 years.
- Let Mary's current age be \( X \) years.

2. **Set Up the Equation Based on Given Information:**
- According to the problem, Adam is 4 times as old as Mary.
- This can be expressed as:
\[ 20 = 4X \]

3. **Solve for Mary's Current Age:**
- Rearranging the equation gives:
\[ X = \frac{20}{4} = 5 \text{ years} \]
- So, Mary's current age is 5 years.

4. **Determine Future Ages:**
- Let \( P \) be the number of years in the future when Adam will be twice as old as Mary.
- In \( P \) years, Adam's age will be:
\[ 20 + P \]
- In \( P \) years, Mary's age will be:
\[ 5 + P \]

5. **Set Up the Equation for Future Ages:**
- We want to find when Adam's age is twice Mary's age:
\[ 20 + P = 2(5 + P) \]

6. **Expand and Rearrange the Equation:**
- Expanding the right side gives:
\[ 20 + P = 10 + 2P \]
- Rearranging this equation leads to:
\[ 20 - 10 = 2P - P \]
\[ 10 = P \]

7. **Calculate Mary's Age After \( P \) Years:**
- Now that we know \( P = 10 \), we can find Mary's age after 10 years:
\[ \text{Mary's age after 10 years} = 5 + 10 = 15 \text{ years} \]

### Final Answer:
Mary will be 15 years old when Adam is twice as old as her.

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